What Makes Sense for PCPs?

[rsterne]

"Overstabilzed" is a relative term, there really is no such thing as too fast a spin for the "tumble resistance" of a projectile.... What it really means is that other factors, such as spin-induced rise and fall in a crosswind due to the "Magnus Effect" and precession caused by an out of balance bullet (CG not aligned with center of form) increase to the point of opening up the group size.... These would not exist in a bullet that is not spinning, and increase as the spin rate increases.... However a bullet not spinning will tumble.... It's about finding the "best" balance between the two....

Bob

[cambriajohn]

I'm wondering how atmospheric conditions effect an air rifle / pellets accuracy. I just saw a  consistently 1 1/2 moa rifle shoot 25 continuous sub moa shots at 75 yards and the only difference from past shooting sessions is that today it was considerably cooler and more humid than normal. 48 degrees F, 64% RH, 2400 ft msl, 27.81 in Hg, 25 cal, BT65, 910 fps. Would a slightly different tune yield these or better results more regularly?

[cambriajohn]

Since I don't want to be the guy who killed this thread, let me ask a different question:

If I understand it correctly, the LASSO competition shoots at steel animal targets at 100 to 300 yards with big bore air rifles. A year or two back the competition was won with a 257 Haley but the rules have been clarified to require at least a 308 now. Using Chairgun a 357 158 gr bullet at 950 FPS would have a 1 MOA vertical change for a 10 FPS spread and a 16 foot vertical drop. So does 300 yards make sense for PCPs?

[rsterne]

No reason why not.... I recently saw a video of a guy with a Haley Scandalous killing a Pop Can at 615 yards.... took him 3 shots, but he got it!....

Bob

[PakProtector]

I suspect we'd have a significantly better idea of the capability of the Scandalous/Charlie ROach combination if that vid was about a half hour long, and there were several pop cans to shoot as well as a sighter target and a target to receive 3-5 shots after the last can. I don't recall if the set up/sighting in was covered or not, or IFF those three shots included ranging/sighting shots too. The only thing I am certain of is that it would take me more than 3 shots to connect...and I have lit a match at 25 yards...
cheers,
Douglas

[Bill G]

Let's do an example, for my .257 Hayabusa, which runs on 3000 psi and has a 28" barrel.... That says I should be able to push a bullet with an SD of 0.196 at 950 fps.... That works out to a weight of 0.196 x 0.257 x 0.257 x 7000 = 90.6 gr (181 FPE) .... The best I've ever done is an 88 gr. bullet at 908 fps (161 FPE) not too far off (89% of target).... Another example would be the Haley Scandalous .257 with a 36" barrel running 4500 psi.... The SD is 0.379, which works out to a bullet weight of 175 gr. at 950 fps (350 FPE).... and Haley has reported that he has managed over 300 FPE (~86% of target).... but I don't actually know what bullet weight and pressure was used to acheive that.... If anything, it would appear that driving the weights produced by this method to 950 fps is a very lofty goal, and very difficult to achieve.... but that's a good thing, because the whole point of this thread was "what makes sense for a PCP".... I think using the weights predicted by this system as an absolute maximum if you want to try and achieve 950 fps (2 FPE/gr.) is a pretty good guide.... For a 24" barrel and 3000 psi, that works out to a maximum SD of 0.168, which gives the following bullet weights....

Bob,  perhaps the missing component to meeting your calculated/ theoretical FPE is in fact the energy used to induce spin.  I would think that if the examples where done with a smooth boer, that the fpe would be much closer to theory.  Also, look at the % difference of the 88gr and the 175gr examples.  the heavier projectile had deminished % and I'll bet the required twist to stabilize the 175gr was more enery than the 88gr.  heavier require more twist and more twist requires more energy and that results in more deviation from theorectical fpe.  Just a thought as to where the energy/efficiency went.   

[PakProtector]

Bill...sonds like a proper math quest. I from the tables of a disc of boolit mass, w( omega ) calculated by speed and twist rate and then E=1/2I* w^2...and I'll get back wid a number soon...

[Tommy]

I did not understand very much of this but i read every word
Tommy

[PakProtector]

so, for a 5 gram, 25 cal boolit, the rotational inertia 1/2mR^2 gives us .00000003 kg-m^2. Lets assume 12" twist so 950 fps gives us 950 rev/sec for total energy of ~0,45 Joule spent spinning it up.
cheers,
Douglas

[Bill G]

How does that correlate to Bobs example, or do we have enough info to asses that? 

BTW Douglas. DUDE YOU ARE A NERD! . An awsome nerd i might add.

Bill

[rsterne]

So, not a lot of energy lost to spinning it up, really.... ~ 0.3 FPE

Bob

[Bill G]

Much lower than I imagined.

[rsterne]

Just had a few more thoughts about the Maximum SD vs Pressure concept.... I'm referring to this graph, which is basically what is the heaviest bullet you could launch at ~ 950 fps for a 24" barrel....
 


It recently occurred to me that you can also use the chart the other way around, to predict how much pressure you need for a given bullet SD (from that 24" barrel).... This might be of some interest if you are curious about what pressures are required for the heaviest pellets in various calibers (as distinct from bullets).... Here are the SDs for those, and the corresponding pressures....

.177 cal - 16.4 gr. - 0.075 - 1400 psi
.22 cal  - 32.4 gr.  - 0.098 - 1800 psi
.25 cal  - 42.7 gr.  - 0.098 - 1800 psi
.30 cal  - 51.2 gr.  - 0.081 - 1500 psi
.35 cal  - 77.8 gr.  - 0.087 - 1600 psi

Since I am interested in the answer, I also did the calculation for my Bob's Boattail's....

.250 cal - 50.6 gr. - 0.116 - 2100 psi
.300 cal - 70.0 gr. - 0.111 - 2000 psi
.308 cal - 79.0 gr. - 0.119 - 2100 psi
.357 cal - 127 gr.  - 0.142 - 2600 psi

This information will come in useful if you are designing, for example, a regulated PCP to shoot pellets (or BBT's) as it will give you the MINIMUM pressure you should consider, assuming you want to be able to use the heaviest pellets available today.... As I think it likely that heavier pellets in .30 and .35 cal will eventually be available, it seems that 1800 psi would be a reasonable pressure to use for the heaviest of pellets.... Remember, these results are not easy to achieve, you will likely need full boresize porting, and it might well be that you may need more pressure or a longer barrel to get to the mid 900s with the heaviest pellets in those lists....

Bob

[Sfttailrdr46]

  I cannot read this thread when tired. I intend to show it to my math nerd computer friend/geek for an English translation, then maybe the math will make more sense as it is just when I think I'm beginning to understand some other bright light adds a new "twist" (slight pun intended)

[rsterne]

It seems like there is a never-ending way that these estimates can be used.... Before I give you my latest however, I need to stress that these are only estimates of what MAY be possible.... Although I have come close with my Hayabusa, it took a slightly longer than 24" barrel to get there.... One of our GTA members, dyotat100, who builds high-powered Condors, has likewise come very close.... I should remind you of the basis for the math behind this....

I started with the bore area, which is caliber (in inches) squared times PI/4.... Then I multiplied by the pressure (in psi) to get the force (in lbs) available to accelerate the pellet/bullet.... I then assumed a 24" barrel, with that push happening over half its length (ie 1 ft.) and that force then became ft.lb. of energy (FPE) that could be produced.... That is where the "estimate" part comes in.... It assumes an equal push over that 1 ft. of distance, at an efficiency of 100%, and then no force for the rest of that 24" barrel.... As it turns out, even with bore-sized porting and the best efficiency I am aware of anybody achieving, this is a lofty goal, but not an unreasonable one.... At least, IMO, it points out what may be a maximum for (at least current) PCPs using air (ie not Helium).... As an example, we can get to these goals for a 24" barrel by using a 28" barrel, (even exceed them slightly) so we're not that far off....

As I worked through this thread (and let me point out that it was a learning and development process), I realized that there were a whole bunch of related things going on.... Since when you push a projectile to 950 fps, the FPE is twice the weight (in grains), it became obvious that if there was a maximum FPE we could reach (for a given pressure in a 24" barrel) then there had to be a maximum weight that could be pushed to 950 fps, and a corresponding Sectional Density (SD).... That led to the graph relating SD to pressure.... Then I realized that it was the product of the pressure and (half) the barrel length (in ft.) that affected the FPE, so for a given pressure you could use a heavier bullet in a longer barrel.... Therefore, any combination of pressure and barrel length (as the product) would have a maximum SD that would have a decent chance of reaching 950 fps.... In the last couple of days, I decided that this could be put into a simple formula in which the pressure, caliber and barrel length could be used to calculate the maximum bullet weight that has a decent chance of reaching 950 fps in a PCP running on HPA.... Here is what I came up with....

W =( P x L/24 x B x B X 3.14159/4 ) / 2
W = P x L x B x B / 61.1
W = P x BV / 48
where W = weight in grains
P = pressure in psi
B = bore in inches
L = length in inches
BV = bore volume in cu.in. (which is L x B x B X PI/4 with all dimensions in inches)

If I may just make a comment about the last formula.... I find it interesting that the weight is proportional to the amount of air.... pressure times barrel volume.... In other words, you can only ask a certain weight of air to do a certain amount of work.... Makes perfect sense to me.... Here are some example cacluations, with their real-life comparisons:

.257 cal, 28" barrel, 3000 psi.... W = 3000 x 28 x 0.257 x 0.257 / 61.1 = 91 gr.... which works out to 182 FPE.... My Hayabusa has reached 908 fps (160 FPE) with a bullet weighing 87.6 gr....

.257 cal, 24" barrel, 3300 psi.... W = 3300 x 24 x 0.257 x 0.257 / 61.1 = 85.6 gr.... which works out to 171 FPE.... dyotat100 managed 170 FPE (925 fps) with an 89.5 gr. bullet....

.257 cal, 32" barrel, 4000 psi.... W = 4000 x 32 x 0.257 x 0.257 / 61.6 = 138 gr.... which works out to 276 FPE.... dyotat100 got 1083 fps (245 FPE) with a 94 gr. bullet....

As you can see, we're not far off the mark.... Heavier bullets can, of course be used, and will likely increase the FPE above estimates, at the expense of not reaching 950 fps.... Conversely, lighter bullets will be able to exceed 950 fps, but likely at reduced FPE, and particularly downrange as transonic drag starts taking it's toll.... As a final, simple formula, here is a good goal for FPE for your next PCP project (on air)....

FPE = P x L x B x B / 30.5 .... With a 30" barrel you can simplify it even further.... FPE = P x B x B (pressure times caliber squared).... For my new 7mm project, that works out to FPE = 3000 x 28 x 0.284 x 0.284 / 30.5 = 222 FPE.... If I can get to 200 FPE with the 95 gr. Bob's Boattail I have designed, and end up with a short string at 950 fps, I'll be a happy camper....

Bob

[Sfttailrdr46]

  Thanks Bob now I have another headache

[Big Bore Bart]

    Quite possibly the remaining energy is taken by the friction between the barrel walls and the pellet/bullet.     This page has the coefficient at .95 for dry, sliding contact.

[rsterne]

The Coefficient of friction is the ratio between the force between the objects and the force required to overcome friction.... If it is 1.0, it means that a 1 lb. object will take 1 lb. of force to slide it.... If it is 0.5, it means that a 1 lb. object will take 1/2 lb. to slide it.... It is really only useful if you had a bullet sitting on a plate of steel, and if the bullet weighed 100 grains, with a coefficient of friction of 0.43, it would take 43 grains of force to slide it.... Lead to cast iron is 0.43 on that chart....

This doesn't really apply to a bullet in a barrel, what you need to know is the force it takes to slide it through the barrel, and also the force it takes to break it loose and start it moving.... You can actually measure these, and when I'm using Lloyd's spreadsheet he has inputs for both values.... What those values are depends on how tight the bullet fits in the bore.... If the bullet is not larger than the groove diameter, the force to keep it sliding is in the 3-10 lb. range, and to start it maybe twice that, depending on the leade angle.... Since in a .308 cal gun running 3000 psi we are dealing with a force of 223 lbs. that is available, we are talking about a measureable amount, but nothing like 50%.... Pellets are more like 2 lbs to start and 1 lb. to keep it moving....

If you want to measure the sliding force required, simply stand your gun on a scale, muzzle down, and push the pellet/bullet with a rod from the breech.... To get the starting force, add weight to the rod until it starts to move and record the weight.... You will be surprised how little force it takes to move a .22 cal or even a .25 cal pellet.... Bullets do take more, and if they are TOO tight, can take a LOT....

Bob

[rsterne]

Once again I lay in bed thinking about this stuff just before arising and came up with yet another way this information can be used.... I made the observation a few days ago that bullets of similar Sectional Density (SD) had very similar lengths, regardless of caliber.... I thought about that this morning, and realized that the weight W of a cylindrical bullet is, of course W= PI x (C^2 / 4) x L x D where C = caliber, L = length, D = density.... and the SD, which is the "weight per unit area" is SD = W / C^2 / 7000.... Both formulas use the square of the caliber, so it ends up that for a cylindrical bullet, the length is proportional to the SD.... Therefore if the SD is fixed (or determined as in the graph above), then the length of a cylindrical bullet having that SD will be a constant, regardless of caliber....

Now for the most part, we don't use cylindrical bullets, as they are very "draggy", so I used the Kolbe Bullet Design Calculator to figure out how much longer our "typical" bullets are than a cylinder of the same weight.... I worked with round-nosed designs and with tangent ogive designs with a decent size Meplat, and found that many bullet designs we use in airguns are about 15% longer than a cylinder of the same weight.... So, I incorporated that as a "fudge factor" into the graph below....



A few important notes here.... This graph is NOT intended for Spitzer bullets, as they will be longer (and yet not much heavier) than a tangent ogive design with a good sized (50-60%) Meplat.... Nor is it intended for roundball.... However, the data is consistent with a lot of the results I have obtained in high-performance PCPs like my Hayabusa and DAQ.... I'm sure you can find bullets that are longer that you can drive at 950+ fps than with the barrel/pressure combinations shown above.... The overall governing factor as to the suitability of a given bullet in a given barrel length and pressure combination will still be its weight.... The above graph will just give you some idea of whether or not a bullet of a given length may be able to be driven close to that 950 fps target velocity....

The interesting data point for a lot of guns in the chart above is for a 24" barrel at 3000 psi.... which suggests a maximum bullet length of 0.60" to reach ~950 fps.... I think you will find that is a pretty challenging, but reachable, target for a high-performance PCP....

Bob

[RHytonen]

..........Well, what about barrels longer than two feet?.... OK, you got me there, in a three foot barrel maybe you should be able to get 50% more FPE than the graph suggests.... You can lug around something that long if you wish....

I know this is going to be controversial, and that's fine.... This is, after all, the Geek Gate, and I expect to have you guys be tough on me.... So, have at it !!!

Bob

Fascinating thread, Bob - Seriously, THANKS!

 But - who says you have to want to "lug it around" all that much?
I'm just suggesting that, for instance at my age and newly limited mobility,
(and possibly at whatever point where one begins to consider truly long range shooting, just for grins)
one does begin to consider there are other ways to acquire a target than to chase it around the woods, across the countryside, or wherever.

There are even truly stationary targets one might consider best approached
from as great a distance as possible, as an advantage.
In such circumstances, a SUPER long range might be the predominant consideration, certainly over mobility - just as shot count, and even efficiency, might not be paramount..

I know I don't get around much anymore (as the song goes) and thus my budding fascination with the possibilities of super long rifles, with 3-4 foot barrels. Then there's that black powder crowd (numerous enough to have their own hunting season,) whose ancestors didn't mind schlepping a five foot rifle even through the woods hunting squirrels... or redcoats....

Rod